A tank used for filling helium balloons has a volume of `0 .3 m^3` and contains (2.0) mol of helium gas at `20 .0^@ C`. Assuming that the helium behaves like an ideal gas.
(a) What is the total translational kinetic energy of the molecules of the gas ?
(b) What is the average kinetic energy per molecule ?

Answer

A, B, C

Explanation

(a) Using `(KE)_(Trans) = 3/2 nRT`
with `n = 2.0 mol and T = 273 + 20 = 293 K,` we find that
`(KE) _(Trans) = 3/2 (2.0) (8.31)(293)`
= `7.3 xx 10^3 J`
(b) The average kinetic energy per molecule is `3/2 kT`
or `1/2 m bar v^2 = 1/2 m bar (v^2)_(rms) = 3/2 kT`
= `3/2 (1.38 xx 10^-23) (293)`
= `6.07 xx 10^-21 J`.